1. Field of the Invention
The present invention relates to a transmission method and a transmitter for use in an ultra wide bandwidth (UWB) telecommunication system, including in an impulse radio system.
2. Description of the Related Art
UWB is a known spread spectrum technique which originates from the radar field and has recently gained considerable interest for use in short-range wireless communication, especially for indoor applications. One of the most promising UWB schemes, proposed by R. A. Scholtz in 1993 and also called Impulse Radio (IR), is based on the transmission of sequences of very short pulses. More specifically, as described in detail further below, Impulse Radio relies upon pulse modulation for modulating the data to be transmitted and ensures multiple access by providing different time-hopping sequences to different users. A comprehensive review of the UWB communication techniques, including impulse radio, can be found in the PhD thesis of T. Erseghe available on the website www.dei.unipd.it/˜erseghe/.
Let us consider an impulse radio system in which data symbols are transmitted to or from different users u, u=1, . . . , Nu. Each user u is allocated a time-hopping pattern defined by a plurality Ns of integers cju, j=0, . . . , Ns−1 where Ns is the number of transmission time intervals (hereinafter referred to as frames) used for transmitting a symbol and the integers cju belong to , [0, Nc−1], each frame being constituted of Nc chips. The UWB signal transmitted to or from a given user u is obtained by modulating a basic sequence specific thereto and that can be expressed as:Su(t)=δu(t){circle around (×)}p(t)  (1)where p(t) is a function giving the waveform of a single pulse, {circle around (×)} denotes the convolution operation and δu(t) is defined as:
                                          δ            u                    ⁡                      (            t            )                          =                              ∑                          j              =              0                                                      N                s                            -              1                                ⁢                      δ            ⁡                          (                              t                -                                  j                  ⁢                                                                          ⁢                                      T                    f                                                  -                                                      c                    j                    u                                    ⁢                                      T                    c                                                              )                                                          (        2        )            in which δ(t) denotes the Dirac function, Tƒand Tc are respectively the duration of a frame and of a chip. δu(t) represents therefore a series of Dirac peaks, each peak being located in a frame (j) and being time shifted by an amount (cjuTc) from the beginning thereof.
The basic sequence of user u is modulated according to a pulse position modulation (PPM) with a data symbol to be transmitted to or from user u. More specifically, to each possible symbol b is assigned a binary encoded sequence bj, j=0, . . . , Ns−1 and the transmitted UWB signal relative to symbol b and user u can be formulated as:
                                          s            u                    ⁡                      (            t            )                          =                              ∑                          j              =              0                                                      N                s                            -              1                                ⁢                      p            ⁡                          (                              t                -                                  j                  ⁢                                                                          ⁢                                      T                    f                                                  -                                                      c                    f                    u                                    ⁢                                      T                    c                                                  -                                                      b                    j                                    ⁢                  δ                                            )                                                          (        3        )            where δ is a time shift which is chosen much smaller than Tc.
Without loss of generality, it may be assumed that the symbols b to be transmitted are simple bits and that the binary sequences assigned to b=0 and b=1 are respectively given by:bj=0,∀j if b=0bj=1,∀j if b=1
In such instance, the transmitted UWB signal corresponding to a bit b can simply be reformulated as:
                                          s            u                    ⁡                      (            t            )                          =                                            S              u                        ⁡                          (                              t                -                                  b                  ⁢                                                                          ⁢                  δ                                            )                                =                                    ∑                              j                =                0                                                              N                  s                                -                1                                      ⁢                          p              ⁡                              (                                  t                  -                                      j                    ⁢                                                                                  ⁢                                          T                      f                                                        -                                                            c                      j                      u                                        ⁢                                          T                      c                                                        -                                      b                    ⁢                                                                                  ⁢                    δ                                                  )                                                                        (        4        )            
More generally, if a sequence of bits bm is transmitted to or from a user u, the corresponding transmitted UWB signal can be expressed as:
                                          s            tr            u                    ⁡                      (            t            )                          =                                            ∑              n                        ⁢                                          S                u                            ⁡                              (                                  t                  -                                      n                    ⁢                                                                                  ⁢                                          T                      s                                                        -                                                            b                      n                                        ⁢                    δ                                                  )                                              =                                    ∑              n                        ⁢                                          ∑                                  j                  =                  0                                                                      N                    s                                    -                  1                                            ⁢                              p                ⁡                                  (                                      t                    -                                          n                      ⁢                                                                                          ⁢                                              T                        s                                                              -                                          j                      ⁢                                                                                          ⁢                                              T                        f                                                              -                                                                  c                        j                        u                                            ⁢                                              T                        c                                                              -                                                                  b                        n                                            ⁢                      δ                                                        )                                                                                        (        5        )            
FIG. 1 shows an example of a basic sequence Su(t) relative to a user u where the pulse waveform p(t) has been zoomed in at the bottom part thereof. In the present example, the basic sequence is constituted of Ns=6 frames, each frame being in turn sub-divided into Nc=16 chips. The beginning of a frame is represented by a longer vertical stroke than the one indicating the beginning of a chip and the arrows referenced 100 to 105 represent the Dirac peaks of the above defined function δu(t), each peak being shifted by an amount given by the corresponding values cju of the time hopping pattern of user u. The basic sequence Su(t) carries a pulse of waveform p(t) at the respective locations of the Dirac peaks. For example, the pulse may be a so-called Rayleigh monopulse the waveform of which is given by:
                              p          ⁡                      (            t            )                          =                              t                          σ              2                                ·                      exp            ⁡                          (                                                -                                      t                    2                                                                    2                  ⁢                                      σ                    2                                                              )                                                          (        6        )            where σ is a value representative of the pulse width. The shape of the waveform has been schematically represented at the bottom of the FIG. 1.
Typically, the pulse width is about 0.5 ns, the frame duration Tƒ is a time of the order of 100 ns and Ts is a time of the order of 1 μs.
When a bit to be sent has a first value, e.g. “0”, the sequence of the user is transmitted as such. Conversely, when said bit to be sent takes the opposite value, e.g. “1”, the positions of the pulses are shifted by a very small amount δ, typically in the order of 50 ps, relatively to the time origin of the basic sequence.
Let us first consider a transmitter sending an UWB signal over a transmission channel to a receiver (where the transmitter can be located either at a base station or at a user terminal). We assume first that a single user is active (either by transmitting or receiving). The received UWB signal can be expressed as:
                                          s            rec                    ⁡                      (            t            )                          =                                            ∑              k                        ⁢                                                            a                  k                                ⁡                                  (                  t                  )                                            ⁢                                                s                  tr                  u                                ⁡                                  (                                      t                    -                                          θ                      u                                        -                                                                  τ                        k                                            ⁡                                              (                        t                        )                                                                              )                                                              +                      w            ⁡                          (              t              )                                                          (        7        )            where k indexes the different propagation paths of the transmission channel, αk(t) and τk(t) are respectively the attenuation coefficients and propagation delays relative to the different propagation paths, θuε[0,Ts[ denotes a time shift between the beginning of the transmission of the UWB signal of user u and a synchronisation time origin, w(t) is the thermal noise of the receiver, assumed to be additive white gaussian (AWGN) with a bilateral spectral power density N0/2.
In practice, for typical indoor applications and slow moving users (that is for moving speeds lower than 10 ms−1), the functions αk(t) and τk(t) can be regarded as constant over a time range of the order of 100 μs (corresponding to the transmission time of about 100 symbols) and therefore the expression of received signal can be simplified as:
                                          s            rec                    ⁡                      (            t            )                          =                                            ∑              k                        ⁢                                          a                k                            ⁢                                                s                  tr                  u                                ⁡                                  (                                      t                    -                                          θ                      u                                        -                                          τ                      k                                                        )                                                              +                      w            ⁡                          (              t              )                                                          (        8        )            where αk and τk are constant values.
Considering now the case of a multi-user system comprising a plurality Nu of transmitters, the received signal can be expressed as:
                                          s            rec                    ⁡                      (            t            )                          =                                            ∑                              q                =                1                                            N                u                                      ⁢                                          ∑                                  k                  q                                            ⁢                                                a                                      k                    q                                    q                                ⁢                                                      s                    tr                    q                                    ⁡                                      (                                          t                      -                                              θ                        q                                            -                                              τ                                                  k                          q                                                q                                                              )                                                                                +                      w            ⁡                          (              t              )                                                          (        9        )            where kq now indexes the propagation paths of the transmission channels between the different transmitters and the receiver in question and αkqq, τkqq are the respectively the attenuation coefficient and the propagation delay relative to the kth propagation path of the qth transmission channel. This expression reflects the typical situation where a plurality of users transmit data symbols over their respective uplink transmission channels to a base station.
Similarly, for a downlink transmission in a multi-user system, since a single transmission channel has to be considered per user, the signal received by user u can be expressed as:
                                          s            rec                    ⁡                      (            t            )                          =                                            ∑                              q                =                1                                            N                u                                      ⁢                                          ∑                k                            ⁢                                                a                  k                  u                                ⁢                                                      s                    tr                    q                                    ⁡                                      (                                          t                      -                                              θ                        q                                            -                                              τ                        k                        u                                                              )                                                                                +                      w            ⁡                          (              t              )                                                          (        10        )            where αku and τku are respectively the attenuation coefficient and the propagation delay of the kth propagation path of the downlink transmission channel relative to user u.
Let us consider the nth bit transmitted to or from user u and denote:
                                          s            0            u                    ⁡                      (            t            )                          =                                            ∑              k                        ⁢                                          a                k                u                            ⁢                                                s                  tr                  u                                ⁡                                  (                                      t                    -                                          θ                      u                                        -                                          τ                      k                      u                                                        )                                            ⁢                                                          ⁢                              when                            ⁢                                                          ⁢                              b                n                                              =                      0            ⁢                                                  ⁢            in            ⁢                                                  ⁢                          (              5              )                                                          (        11        )            and
                                          s            1            u                    ⁡                      (            t            )                          =                                            ∑              k                        ⁢                                          a                k                u                            ⁢                                                s                  tr                  u                                ⁡                                  (                                      t                    -                                          θ                      u                                        -                                          τ                      k                      u                                                        )                                            ⁢                                                          ⁢                              when                            ⁢                                                          ⁢                              b                n                                              =                      1            ⁢                                                  ⁢            in            ⁢                                                  ⁢                          (              5              )                                                          (        12        )            Defining vu(t)=s1u(t)−s0u(t), it can be shown that the optimal decision criterion at the receiving side is based on the decision variable:
                                          b            ~                    n                =                              ∫                          t              n              min                                      t              n              max                                ⁢                                                    s                rec                            ⁡                              (                t                )                                      ⁢                                          v                u                            ⁡                              (                t                )                                      ⁢                          ⅆ              t                                                          (        13        )            where
      t    n    min    =                    n        ⁢                                  ⁢                  T          s                    +              θ        u            +                        min          k                ⁢                              (                          τ              k              u                        )                    ⁢                                          ⁢                      and                    ⁢                                          ⁢                      t            n            max                                =                  nT        s            +              θ        u            +                        max          k                ⁢                  (                      τ            k            u                    )                    +      δ      define the bounds of reception time window for the nth bit of user u.
It should be noted that the decision variable bn can be regarded as the output of a filter matched to the impulse response of the transmission channel of user u. The bit estimate {circumflex over (b)}n is obtained as follows:{circumflex over (b)}n=0 if {tilde over (b)}n≦0 and {circumflex over (b)}n=1 if {tilde over (b)}n≧0  (14)
One of the critical issues addressed in the prior art is the choice of a set of basic sequences exhibiting good auto-correlation and cross-correlation properties. More specifically, denoting respectively
                                          π            u                    ⁡                      (            t            )                          =                                            S              u                        ⁡                          (              t              )                                ⊗                                    ∑              n                        ⁢                          δ              ⁡                              (                                  t                  -                                      nT                    s                                                  )                                                                        (        15        )            the function obtained by periodically repeating the basic sequence of user u and Cu,u′(τ) the correlation function between πu(t) and πu′(t), i.e.
                                          C                          u              ,                              u                ′                                              ⁡                      (            τ            )                          =                              ∫                          T              s                                ⁢                                                    π                u                            ⁡                              (                t                )                                      ⁢                                          π                                  u                  ′                                            ⁡                              (                                  t                  +                  τ                                )                                      ⁢                          ⅆ              t                                                          (        16        )            the choice of a set a of sequences is based on the quality criteria:
                              S          max                =                                            max                                                u                  ∈                  σ                                ,                                  τ                  ≠                  0                                                      ⁢                                          (                                                      C                                          u                      ,                      u                                                        ⁡                                      (                    τ                    )                                                  )                            ⁢                                                          ⁢                              and                            ⁢                                                          ⁢                              C                max                                              =                                    max                              u                ,                                                      u                    ′                                    ∈                  σ                                ,                                  τ                  ∈                                      [                                          O                      ,                                              T                        s                                                              ]                                                                        ⁢                          (                                                C                                      u                    ,                                          u                      ′                                                                      ⁡                                  (                  t                  )                                            )                                                          (        17        )            
The first quality criterion is a low value of Smax, which means that the respective auto-correlation functions of the basic sequences of the different users exhibit low level side-lobes, improving thereby synchronisation at the receiving side. The second quality criterion is a low value of Cmax, which favours the reduction of multi-access interference. It will be appreciated that Cu,u′(τ) is representative of the overlap between the two delayed basic sequences and essentially depends upon the number of coincidences (or hits) between delayed versions of the hopping patterns of users u and u′.
FIGS. 2A and 2B illustrate the situation where a basic sequence of a given user u interferes with a basic sequence of another user u′ at the receiving side. This could be the case if, for example, the two sequences have travelled along different propagation paths, although their respective transmitters are synchronised. This could also be the case, if these sequences have travelled along the same propagation path but their respective transmitters are not synchronised (or, alternatively, neither their propagation paths are the same nor their respective transmitters are synchronised).
As a matter of example, while FIG. 2A shows a case where the collision can be resolved by the receiver, FIG. 2B shows a severe collision of sequences with a large score of hits leading to a high probability of false detection. Such type of collision will be hereinafter referred to as catastrophic.
In practice, the risk of collision between received sequences is not negligible and can dramatically increase the bit error rate of the communication affected by the collision. This is all the more significant since the characteristics of the transmission channels are likely to be constant in an indoor environment (e.g. the transmitter(s) and receiver(s) are fixed) and therefore a catastrophic collision may repeat at quite a high rate.